International Journal of Advances in Engineering & Technology, May 2013. ŠIJAET ISSN: 2231-1963 Step2: Perform DCT on the LH band of DWT decomposition, which is denoted by đ?‘“đ??ˇđ??śđ?‘‡ . Step3: Apply SVD on đ?‘“đ??ˇđ??śđ?‘‡ . đ?‘†đ?‘‰đ??ˇ đ?‘†đ?‘‰đ??ˇ đ?‘†đ?‘‰đ??ˇ đ?‘†đ?‘‰đ??ˇ đ?‘“đ??ˇđ??śđ?‘‡ = đ?‘ˆđ??ˇđ??śđ?‘‡ ∗ đ?‘†đ??ˇđ??śđ?‘‡ ∗ đ?‘‰đ??ˇđ??śđ?‘‡
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Step4: Perform SVD on watermark image. T WSVD = UW ∗ SW ∗ VW (16) Step5: Modify the single values of reference image with the singular values of watermark as đ?‘†đ?‘‰đ??ˇ ∗ đ?‘“đ?‘†đ?‘‰đ??ˇ = đ?‘†đ??ˇđ??śđ?‘‡ + β ∗ SW (17) Where, β gives the watermark depth. Step6: Perform inverse SVD, ∗ SVD SVDT ∗ đ?‘“đ?‘–đ?‘ đ?‘Łđ?‘‘ = UDCT ∗ đ?‘“đ?‘†đ?‘‰đ??ˇ ∗ VDCT (18) Step7: Perform inverse DCT and DWT to construct the modified reference image, denoted by .
Again
is segmented into blocks of size p1 Ă— p2 and mapped onto their original positions for
constructing the watermarked image. We save the positions of the significant blocks and reference image for the extraction process. 3.3.2. Watermark Extraction Procedure Step1: Using the positions of significant blocks, make the reference image from the watermarked đ?‘Š image, denoted by đ??šđ?‘&#x;đ?‘’đ?‘“ . W Step2: Perform DWT and DCT on watermarked reference image, Fref . Which is denoted by . Step3: Perform SVD transform on
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đ?‘Š đ?‘Š đ?‘Š đ?‘Š đ?‘“đ?‘&#x;đ?‘’đ?‘“ = đ?‘ˆđ?‘&#x;đ?‘’đ?‘“ ∗ đ?‘†đ?‘&#x;đ?‘’đ?‘“ ∗ đ?‘‰đ?‘&#x;đ?‘’đ?‘“ Step4: Extract the singular values of the watermark. đ?‘Š SVD đ?‘†đ?‘&#x;đ?‘’đ?‘“ − SDCT đ?‘† đ?‘’đ?‘Ľđ?‘Ą = β Step5: Obtain the extracted watermark as: đ?‘‡ đ?‘Š đ?‘’đ?‘Ľđ?‘Ą = đ?‘ˆđ?‘Š ∗ đ?‘† đ?‘’đ?‘Ľđ?‘Ą ∗ đ?‘‰đ?‘Š
IV.
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RESULT ANALYSIS
The performances of proposed colour image watermarking algorithms were evaluated with Lena, Mandrill, Home and peppers of size 512 x 512. This has shown in table 1. For the embedding process two gray scale watermark images were used in this experiment. These watermarks were embedded into the three components (RED, GREEN and BLUE) of the RGB colour images. The three algorithms are applied for each colour component for watermarking process. For DCT-SVD algorithm the watermark size was 256 x256, for DWT-SVD and DWT-DCT-SVD algorithms watermark size was 128 x 128. The three algorithms, which are discussed above are implemented on Lena as a cover image and copy as a watermark image. These algorithms are tested against various attacks as mentioned above. This has shown in table2. The performance of proposed algorithms was carried out with two measures. One is imperceptibility, means that the perceived quality of the colour image should not be distorted by the presence of the watermark. As a measure of the quality of a watermarked image, the peak signal to noise ratio (PSNR) is typically used. Second one is robustness, is a measure of the immunity or resistance of the watermark against attempts to remove or degrade it from the watermarked colour image by different types of digital signal processing attacks. The similarity between the original watermark and the extracted watermark from the attacked watermarked image was measured by using the correlation factor , which is computed using the following Equation: đ?œŒ(đ?‘¤, đ?‘¤ Ěƒ) =
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∑đ?‘ Ěƒ đ?‘–=1 đ?‘¤âˆ—đ?‘¤ đ?‘ Ěƒ2 2 √∑đ?‘ đ?‘–=1 đ?‘¤ √∑đ?‘–=1 đ?‘¤
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Vol. 6, Issue 2, pp. 888-902